Is there any way to simulate connected solid objects using cloth physics or similar
This can be achieved with Cloth physics or Soft Body physics.

Starting with Soft Body (since it's more versatile), the first step is to create the mesh - effectively two joined cubes. So starting with the default cube, select it and use Ctrl+D to duplicate it and position it in the desired location. Select both cubes (select one, hold Shift while clicking the other) and press CtrlJ to join them into a single object. NOTE : You should select the 'child' cube first (the one you want to have dragged about by the other), followed by the 'parent' - this way the origin of the combined mesh will be at the centre of the 'parent' cube.



We could use Soft Body options to keep the cubes from being distorted. However, this will interfere with the bending motion we want to produce. Therefore, we'll add 'struts' to the mesh to give it rigidity.

Go into Edit mode (Tab) and select wireframe view (Z). Select two opposing corners of a face and press F to create an edge between them.

Repeat this for every face on each cube - this will make each cube rigid without having to use the Soft Body 'Stiff Quads' or 'Bending' options, leaving them to be adjusted for controlling the bendiness between the cubes.



To join the cubes together, select each nearby pair of vertices in turn and again press F to create an edge between each.



Whilst still in Edit mode, select all the vertices of the 'parent' cube, create a new Vertex Group (named 'pin') and click 'Assign' to assign those vertices to the group.



Now swap back to Object mode (Tab) and in the Physics panel add Soft Body. In the Soft Body Goal settings set the Default Strength and Stiffness to their maximum and set the Vertex Group to the 'pin' group created earlier. In Soft Body Edges set the Pull and Push springs up to their maximum - this will force the edges to be a fixed length, locking the shape of the cube due to the 'struts' that were added earlier.

Now animate the mesh as desired - you should get the 'child' cube following and adjust the Bending Stiffness spring in the Soft Body Edges to get the desired stiffness of the joint. Switch off gravity (set the Soft Body Field Weight to zero) and enable Soft Body Self Collision if required. Optionally adjust the Soft Body Solver settings (eg, increase Min Step) if necessary. You can also adjust the Friction (on the main Soft Body properties) to calm down the bounciness if required.

This can produce the following result :





Cloth physics is fairly similar but needs a minor tweak to the mesh - since the cloth uses the presence of faces rather than edges to determine how the mesh behaves. So using the same mesh (ie, two cubes with added 'struts'), in Edit mode, select the 4 vertices between the two cubes and press F to create a  face.



Instead of Soft Body (remove it if using the same model), add Cloth. On the main Cloth properties panel, enable Pinning and use the same 'pin' vertex group as used for the Soft Body version. Disable Gravity in the Cloth Field Weights and enable Self Collision in the Cloth Collision panel.

You can use the Cloth panel to adjust the behaviour of the simulation. It's not as tunable as the Soft Body simulation but you should be able to get reasonable results - although you might still get some distortion of the cubes at high speed.







Blend files included :

Soft Body 

Cloth